cp's OEIS Frontend

A317723 Round-robin tournament numbers: The number of possible point series for a tournament of n teams playing each other once where n points are awarded to the winning team and 1 to each in the case of a tie. A team winning more games than another always has a higher point score.

%I A317723 #32 Sep 16 2024 12:49:06
%S A317723 1,2,7,40,367,4828,82788,1750152
%N A317723 Round-robin tournament numbers: The number of possible point series for a tournament of n teams playing each other once where n points are awarded to the winning team and 1 to each in the case of a tie. A team winning more games than another always has a higher point score.
%C A317723 The 3-point rule is equivalent to that for football (A064626).
%C A317723 The classical 2-point rule is equivalent to that for chess tournaments (A007747).
%H A317723 Donghwi Park, <a href="https://gist.github.com/gwahak/8e96bfe2438679aca0af7c33750916cc">source code for a(5)</a>
%e A317723 a(1)..a(4) are the same as in A064626.
%o A317723 (Python)
%o A317723 def play(ps, n, r, i, j):
%o A317723     if j>=n:
%o A317723         ps.add(tuple(sorted(r)))
%o A317723     else:
%o A317723         (ni,nj) = (i,j+1) if j<(n-1) else (i+1,i+2)
%o A317723         s=list(r)
%o A317723         s[i]=r[i]+n; play(ps,n,s,ni,nj)
%o A317723         s[i]=r[i]+1; s[j]=r[j]+1; play(ps,n,s,ni,nj)
%o A317723         s[i]=r[i]  ; s[j]=r[j]+n; play(ps,n,s,ni,nj)
%o A317723 def A317723(n):
%o A317723     ps=set()
%o A317723     play(ps,n,[0]*n,0,1)
%o A317723     return len(ps)
%o A317723 # _Bert Dobbelaere_, Oct 07 2018
%Y A317723 Cf. A007747, A064626.
%K A317723 nonn,more,hard
%O A317723 1,2
%A A317723 _Donghwi Park_, Aug 05 2018
%E A317723 a(6)-a(8) from _Bert Dobbelaere_, Oct 07 2018